   Chapter 17.6, Problem 17.15CYU

Chapter
Section
Textbook Problem

Silver nitrate (0.0050 mol) is added to 1.00 L of 1 00 M NH3. What is the concentration of Ag+ ions at equilibrium? A g + ( a q ) + 2 N H 3 ( a q ) ⇄ [ A g ( N H 3 ) 2 ] + ( aq )   K f = 1.1   ×   10 7

Interpretation Introduction

Interpretation:

The concentration of Ag+ ions present at the equilibrium is to be calculated.

Concept introduction:

Some metal ions when present in an aqueous solution containing anions or neutral species called Lewis base or ligands having a tendency to donate electron pairs to metal ions then complex ion formation will take place. Complex ions are stable and thus formation of these increase the solubility of the salt containing the metal ions same as in complex ions.

Example of metal ions that form complex ions include Ag+,Cd2+,Fe2+,Zn2+,Ni2+ etc.

Example of Lewis bases includes,NH3,OH etc.

The complex ion remains in equilibrium with the metal ion and the ligand called complex ion formation equilibrium and the equilibrium constant is called as formation constant Kf.

A larger value of Kf implies that the complex ion formed is more stable. Kf is the measure of the strength of the interaction between the metal ions and the lewis base to form the complex ion.

Kd is the dissociation constant of the complex ion and its value is equal to the inverse of the formation constant value of the same complex because dissociation of a complex is just reverse of the formation of the complex. A larger value of Kd implies less stable complex ion.

Kf=1Kd (1)

For example for general complex ion formation reaction,

xM+yL[MxLy]

Kf and Kd can be given as,

Kf=1Kd=[MxLy][M]x[L]y

Here,

• [MxLy] is the equilibrium concentration of complex ion.
• [M] is the equilibrium concentration of metal ion.
• [L] is the equilibrium concentration of the ligand.
• x and y are the coefficients of metal ion and ligand respectively.
Explanation

The concentration of Ag+ ions present at the equilibrium is calculated below.

Given:

The initial concentration of NH3 is 1.0 M.

The concentration of AgNO3 solution is 0.0050M.

The value of formation constant,Kf, for [Ag(NH3)2]+ is 1.1×107.

The high value of formation constant for the complex ion [Ag(NH3)2]+ implies that the complex formed is very stable. So all the Ag+ ion from AgNO3 will react with NH3 such that the initial concentration of the complex will be equal to the initial concentration of AgNO3. The complex ion then dissociates to give Ag+ ion and two NH3 molecules in solution.

The complex will dissociate as follows,

[Ag(NH3)2]+(aq)Ag+(aq)+2NH3(aq)

The value of dissociation constant, Kd for [Ag(NH3)2]+ is given by equation (1).

Kd=1Kf

Substitute 1.1×107 for Kf.

Kd=11.1×107=9.09×108

The concentration of [Ag(NH3)2]+ is 0.0050M.

The concentration of NH3 is calculated as below,

[NH3]=orignal concentration of NH3(2×0.005)=10.01=0.99 M

The ICE table for the dissociation of [Ag(NH3)2]+ is as follows,

Equation[Ag(NH3)2]+Ag++2NH3Initial(M)0.00500.99Change(M)x+x+2xEquilibrium(M)0

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